New Chromatic Monuments - Final Probability Analysis (500 L1 Sample)

[Night_Guy]

Hey everyone,

Like many of you, I’m loving the new colorful monuments! They look awesome.

I was curious if the new colors changed the probabilities, especially for rares. I decided to run a test and make a large batch of Level 1 (L1) monuments to see what the numbers said. I’ve just finished my test after 500 makes.

A Note on Evolution Paths

The test was for L1 crafting, but from what I’ve seen, the fundamental evolution paths are still the same. The color a monument starts with at L1 now determines the new colorful evolution path it will follow.

TL;DR: The 10% Rare Chance is Confirmed

The data strongly suggests the new colors were added to the ‘non-rare’ pool, and the fundamental rare chance remains the same.

Rare is still rare, holding at the historical 10% total chance.

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The Final Test Data (Sample Size: 500)

I made 500 L1 monuments. Here is the summary of my results:

• Total Rare (Yellow) Monuments: 39
• Total Non-Rare (Color) Monuments: 461

This gives an observed rare rate of 39/500=7.8%. This is well within the expected statistical variance for a true 10% probability.

Here is the complete table of my results:

Monument Name	Color	Count	Photo
Lustrous Fountain Crystal	Yellow Rare	10
Golden Mesa Crystal	Yellow Rare	7
Shining Forgotten Crystal	Yellow Rare	10
Gleaming Reservoir Crystal	Yellow Rare	12
Total Rares		39
Classic Fountain Crystal	Blue	32
Ancestral Mesa Crystal	Blue	23
Ancient Forgotten Crystal	Blue	26
Arid Reservoir Crystal	Blue	23
Arcane Fountain Crystal	Purple	26
Mystic Mesa Crystal	Purple	31
Shadowed Forgotten Crystal	Purple	26
Ethereal Reservoir Crystal	Purple	32
Grand Fountain Crystal	Green	26
Vast Mesa Crystal	Green	23
Desert Forgotten Crystal	Green	24
Deep Reservoir Crystal	Green	29
FIery Fountain Crystal	Red	37
Burning Mesa Crystal	Red	36
Cursed Forgotten Crystal	Red	39
Molten Reservoir Crystal	Red	28
Total Non-Rares		461
GRAND TOTAL			500

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The Mathematical Breakdown

Based on this data, the system is the results are consistent with a 10% rare pool and a 90% non-rare pool:

1. The ‘Rare’ Pool (10% Total Chance)

This 10% slice of the probability is reserved exclusively for the 4 rare yellow monuments.

• Chance for any rare: 10% (or 1 in 10 makes)
• Assuming an equal split, the chance for one specific rare monument is: 10% / 4 types = 2.5% (or 1 in 40 makes)
• Data Check: With 500 makes, the expected count (the average) for each rare is 500 * 2.5% = 12.5.
• Result: My observed counts of 10, 7, 10, 12 are all clustered very well around this expected value of 12.5.

2. The ‘Non-Rare’ Pool (90% Total Chance)

This is where all the new colorful monuments were added. The other 90% of outcomes are spread across these 16 non-rare items (4 series x 4 colors).

• Chance for any non-rare: 90% (or 9 in 10 makes)
• Assuming an equal split, the chance for one specific non-rare monument is: 90% / 16 types = 5.625% (or roughly 1 in 18 makes)

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Standard Deviation Confirms It

To be extra sure, I ran the standard deviation on the non-rare pool to see if my counts were “normal” or just a lucky fluke.

• The expected count (the average) for each non-rare item was 28.125 (from 500 * 5.625%).
• The standard deviation (SD) for this test is approx. 5.15.
• This means we can expect approx. 95% of the results for each item to fall within 2 standard deviations of the average (28.125).
• Expected 95% Range: 28.125 +/- (2 * 5.15) = [17.8, 38.4]

Now look at my 16 non-rare counts: (32, 26, 23, 23, 26, 31, 26, 32, 26, 23, 24, 29, 37, 36, 39, 28)

This is a textbook result. My lowest count (23) is well above the 17.8 floor. My highest count (39) is just outside the 95% range, which is perfectly normal (we expect 1 in 20 results to fall outside this range). All 16 counts are well within the 3-sigma range (99.7% of results).

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Deeper Statistical Validation (For the Math Fans)

For those who love the hard numbers, here is a more rigorous statistical validation of the data, which confirms the model is a great fit.

• Overall rare rate: 39/500 = 7.8%.

  • For n=500, p=0.10, the binomial SD is sqrt(n*p*(1-p)) = sqrt(45) approx. 6.71.

  • Z-score for 39 rares: (39-50) / 6.71 approx. -1.64 → well within the 95% band (about 36.9 - 63.1).

  • Wilson 95% CI for the observed rate: 5.76% - 10.49%, which includes 10%.

• Split among the 4 rares:

  • If the rare pool is equal (2.5% each), expected per rare over 500 makes is 12.5. The counts (10, 7, 10, 12) are fine.

  • A quick chi-square test for equal split conditional on 39 rares (expect 9.75 each) gives chi-square approx. 1.31 with df=3 → no issue.

• Non-rare items (16 types):

  • If the 90% pool is equally split, p=0.05625 each → expected 28.125 with SD sqrt(n*p*(1-p)) approx. 5.15.

  • The 16 counts: (32, 26, 23, 23, 26, 31, 26, 32, 26, 23, 24, 29, 37, 36, 39, 28)

  • 95% range approx. 17.8 - 38.4; having one entry at 39 just outside is perfectly normal (approx. 1 in 20 outside). All are comfortably within 3-sigma (approx. 12.7 - 43.6).

• Whole-table fit:

  • Testing the 20-category table against the “10% equally split across 4 rares + 90% equally split across 16 non-rares” model gives chi-square approx. 18.1 with df=19 → do not reject (fits fine).

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Conclusion

You can safely make the new monuments knowing that the ‘rare’ pool is separate and its 10% chance has not been diluted. The 10% rare / 90% non-rare split is statistically solid.

Hope this data helps everyone!

[cw2988]

Great analysis Night Guy, this roughly tracked with my experience. I already had complete sets of the yellow and stopped making monuments once I had 4 each of all the new ones so wasn’t closely monitoring yellow, I probably had 1-2 of each and just guessed 5% for all, so it turns out my guesstimate was out by 2.5% for yellow.

The layman way I interpreted rarity relative to the previous system was it appeared the yellow are now “less” rare than previous given there is now a greater number of total monuments possible:

In the previous system there was 2.5% (10/4) for any yellow compared to 22.5% (90/4) for any other.

In the current system there is now 2.5% (10/4) for any yellow compared to 5.625% (90/16) for any other.

I’m sure I’m committing multiple mathematical faux pas with that assertion though .

Generally speaking, if you are going for a rainbow city build it is quite easy to get all required, while a city of several particular monuments will take a long time to collect.

[Elanor]

Thanks for that - as I expected.
The yellows are still as rare as they were before, there are just more options for the non-rare.

[NashRivers]

So far for me, When I evolve a rare Yellow L1 monument, I use a mix of random L1’s (Different types and colors) to evolve the yellow L1 to a Yellow L2 and it seems to work each time. What I am evolving seems to stay with the same color. I have evolved some L1 choromatic ones into a L2 chormatic, and then used that in a mix to evolve a L2 Rare yellow into a L3 Rare yellow and again, seems to work as before.

The new colors are amazing and the different looks of the monuments will open up more possibilities when trying to imagine a new color layout.

[Night_Guy]

I’ve been noticing something since adding all the new L1 monuments. I’ve only had L4 monuments before this, so it’s a new observation for me.
It seems like the new buildings might have diluted the green prize pool for my L4 monuments. I’m seeing way fewer large gems and passes from my L4s now - in fact, I’ve gotten like none in the last 3-4 collections from them. It looks like the green prizes are mostly landing on that batch of 500 L1 monuments I made.
So, it appears what I suspected is true: for the best prizes, you really want to stack your city with as many L4 monuments as possible.

[PB234]

@NashRivers You will not see a change with the Yellow monument paths. They are still the same before the Chromatic was added. But there are some of the old paths that are realigned with these additions. For instance the path the the Exa Dimension Crystal. From the initial Arid Reservoir the next level produced the Space Tower (which was green) then the Overclocked (which is purple), then to the Exa. Not the Ancestral path produces the Sky Tower which is blue. So the Space Tower and Overclocked monuments are not in 2 different paths to monuments. It is just a change to understand if you are looking to end up with a particular L4 monument. The basis of evolving is still the same. The L1 you start with leads to the end L4 of that path. That is where CW2988 image in a different Help Topic discussion helps understand each path.

[Night_Guy]

@NashRivers I suppose the easy way to see it now is that the evolution path just follows the color.

[txmaryk99]

I love the dullness of your analysis

I did have a blue level 15 that evolved to a purple level 23 last week, but that is ok I plunked it down and will try again for the blue 23 and then move the purple 23 to the path when I get the 7, 10, and 15. It is all part of the game right

I already had my rare golds all evolved to 23’s.

I am enjoying the new colors and the hunt to complete them to 23’s.

And I am sorry that your quest to help us understand the new monuments has resulted in you receiving fewer higher prizes.

[Night_Guy]

@txmaryk99 Haha, glad my riveting analysis kept you on the edge of your seat!

That’s frustrating about your blue L15 turning purple, but you’ve got the right attitude! It’s all part of the hunt.

The evolve path was a little confusing in the beginning due to the way previous rare and non-rare monuments’ evolution paths worked. Now that they added more colors, it just makes sense that the color a monument starts with at L1 now determines the new colorful evolution path it will follow.

And no worries at all about the smaller prizes! It’s all part of the testing. Thank you for mentioning it though.

Have fun building! Would love to see what others come up with.

[CaptainCrow]

Well i for one love the info NG, keep it up sir!!! I don’t care if its dull lol.

[PB234]

Well that is an interesting observation. I didn’t realize the game would direct green boxes away from any particular building. I just thought each one has a cycle on when it will produce a green box. Though I can’t say that is true either since I have tracked my T17-19 and L4 monuments for the last month to try to see what mine produce. I wanted to have a personal data set to understand this.

[PB234]

I evolved my first L1 chromatic monument to L2 today. I am looking forward to getting them to L3 at the same time working on getting each of these built out to L4. I want to see each of the final results in my city. Maybe I will make some kind of real plan for cosmetics once I get there.

[River_girl]

OMGosh, thank you Night Guy! I am so glad to hear someone else mention their L4 monument prize pool has been seriously reduced SINCE adding all the new lower level colorful monuments. I thought my city had hit a new low because it was getting too old to produce any longer and that seriously worried me. LOL. So once I evolve all these lower new color monuments I’m collecting, I should see my city replenish again?

[Night_Guy]

Hey @River_girl, I believe so, but I can’t be 100% certain. I evolved most of those 500 L1s right away after I noticed the prize pool change.

I can say that for me, it’s much better now that I’ve increased the total percentage of L4 monument buildings in my city to over 50%. It was under 15% prior. I’m working on getting it above 80% eventually.

[PB234]

@Night_Guy Hi. So having L4’s as a major percentage of your overall buildings plays a piece in collecting higher Green Boxes?

[Night_Guy]

Hey @PB234,

Yes, that’s exactly what I’ve observed.

For the longest time, I only made one, maybe two, L4 monument(s) at a time, so I got accustomed to my usual green prizes. When I added all 500+ L1 chromatic monuments at once, things changed: my total green prizes went from around 50 to 80, but they seemed to be randomly distributed across all my buildings.

Now, I’m sure the HMP (Honeymoon Period) came into play at this point, especially since I added ~100K in gem value to a city that already surpasses that by many folds. Still, you can make some educated guesses based on the numbers.

Here’s the main thing: even though I added 500+ buildings to my ~200 building city (a 3.5x increase in count), my green prizes didn’t increase by 3.5x. This makes me believe the total quantity of green prizes is determined by the total gem value of your city, not just the building count.

Therefore, to get better green prizes, you want those randomly-assigned prizes to land on the L4s. The more L4s you have as a percentage of your total buildings, the better your chances are that those valuable prizes will land on a high-reward building.

• Gem/Pass prize on an L4: You get at least 85 gems/passes + 100 coins (every 6 hours, post-HMP). There is also a 3x multiplier on these and the reward grows over time.
• Charm on an L4: Holiday Wine or Golding Playing Card + 100 coins every 6 hours.
• That same prize on an L1: You get much less.
• L4 with no green prize: Just gives its standard 8.5M coins every 6 hours.

I hope that makes sense! These are just my observations; others could have different results due to the many variables.

[PB234]

Hi @Night_Guy All observations are worth noting and gives me another avenue to try. I am still heavy on L1, L2, L3 though at the point to consider evolving more L4’s. So this might be a good time to work it into my plans to watch the results. I know my total city Gem value is $2.17 bil so know I am at that target level. Now I just have to fit it into my schedule and make it happen. Thanks very much for your time.

[River_girl]

I really appreciate your quick reply and interesting L4 percentage observations! I was randomly trying to get an example of each monument in each color, but I may need to be more precise about my approach… Another change (a good one!) that happened while accumulating all the new monuments is that my TB party passes increased noticeably. Do you have any percentage observations around party passes/gem TB’s and monuments you’d like to share - or are they more random? I am really enjoying the PP increase and would hate to lose it by my experimentations. LOL

THANKS AGAIN for your insights, they are very helpful - River

[Night_Guy]

Hey @PB234, I usually go by stats and crowd consensus, especially when enough reliable people report the same thing. This game has so many variables, and with random updates, things change often. My original tips post is pretty outdated now, though I’m working on updating it. It’s like ‘Who Wants to Be a Millionaire’ - the ‘audience’ is usually correct plus some sort of fuzzy logic you need to apply along with some maths lol.

For example, I’m now getting reports that the Charoite (purple) and Sapphire (blue) dragonets might be appearing in both Bust Tier 5 and Bust Tier 6 parties. The chance seems different now that the offer is indefinite. I’m not sure if it’s tied to the host, their city size, or if they already have a dragonet or that specific dragonet. I do know the last 5 of my 10x unicorn parties (Tier 7) all yielded a Jet dragonet according to the attendees. But, I suppose it doesn’t matter much yet since it’s not that much harder to bust Tier 6 parties, and so far, only one host has mentioned the attendees getting both Charoite and Sapphire dragonets in one party.

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Hey @River_girl, regarding your question about TB prizes:

Your city has prize tiers that work with random multipliers from 0.5x up to 10x for the TBs (Treasure Boxes). New buildings, especially with the HMP (Honeymoon Period), give a bigger boost to your TB tier. Even in a maxed-out city, I’ve noticed that adding new buildings still boosts the TB on average.

However, be careful with when you add them. If you add new buildings between 6 PM and 8 PM Pacific Time , or around 10 PM to 11:59 AM , you might get caught in some sort of tier reset or prize downgrade.

Please take a look at this discussion from this post down regarding the treasure box - Tips and Tricks for Beginners and Veterans - #80 by Night_Guy